About the rate function in concentration inequalities for suprema of bounded empirical processes

Abstract : We provide new deviation inequalities in the large deviations band-width for suprema of empirical processes indexed by classes of uniformly bounded functions associated with independent and identically distributed random variables. The improvements we get concern the rate function which is, as expected, the Legendre transform of the suprema of the log-Laplace transform of the pushforward measure by the functions of the considered class (up to an additional corrective term). Our approach is based on a decomposition in martingale together with some comparison inequalities.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01587060
Contributeur : Antoine Marchina <>
Soumis le : jeudi 14 septembre 2017 - 00:40:15
Dernière modification le : jeudi 11 janvier 2018 - 06:25:42

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  • HAL Id : hal-01587060, version 2

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Antoine Marchina. About the rate function in concentration inequalities for suprema of bounded empirical processes. 2017. 〈hal-01587060v2〉

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